Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method

Bierig, Claudio; Chernov, Alexey

doi:10.1016/j.jcp.2016.03.027

Cited by 55 publications

(43 citation statements)

References 22 publications

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“…The same holds for the estimation of PDFs. However, recent works have proposed different ways to estimate PDFs and shown very promising results . Extensions for sensitivity analysis have also recently been made …”

Section: Frequentist Approachesmentioning

confidence: 99%

“…However, recent works have proposed different ways to estimate PDFs and shown very promising results. [21,22] Extensions for sensitivity analysis have also recently been made. [23] Since its introduction for geometric integration, [1] MLMC has been applied to several problems, such as path simulations in finance, [2] subsurface flow, [24][25][26] and inviscid incompressible flow.…”

Section: Multilevel Monte Carlomentioning

confidence: 99%

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Multifidelity approaches for uncertainty quantification

et al. 2019

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The aim of this paper is to give an overview of different multifidelity uncertainty quantification (UQ) schemes. Therefore, different views on multifidelity UQ approaches from a frequentist, Bayesian, and possibilistic perspective are provided and recent developments are discussed. Differences as well as similarities between the methods are highlighted and strategies to construct low‐fidelity models are explained. In addition, two state‐of‐the‐art examples to showcase the capabilities of these methods and the tremendous reduction of computational costs that can be achieved when using these approaches are provided.

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Section: Frequentist Approachesmentioning

confidence: 99%

Section: Multilevel Monte Carlomentioning

confidence: 99%

Multifidelity approaches for uncertainty quantification

et al. 2019

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“…The failure data sequence is used to simulate the failure distribution based on the median rank experience [11], lognormal distribution, Weibull distribution and maximum entropy probability distribution [12,13], then the reliability function of each failure model can be acquired. Among them, the experience value model is simple and reliable without parameter estimation, but the true value of reliability estimation result is discrete and wavy, difficult to provide the continuous assessment.…”

Section: Introductionmentioning

confidence: 99%

Reliability Calculation of Product Failure Data (Part I: Theory)

Xia¹,

Chang²,

Li³

et al. 2016

Proceedings of the 2016 International Conference on Sensor Network and Computer Engineering

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“…Whether in seeking transition paths to overcome large free energy barriers in molecular simulations or in assessing the extremely small probabilities of failure in engineering systems [8], we need new tools that are capable of directing our simulations or data-acquisition mechanisms to the most informative regimes [9].…”

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confidence: 99%

“…Model-selection issues arise prominently in obtaining reduced or coarse-grained descriptions of physical models (e.g., in molecular dynamics or quantum mechanical models), and along these lines the expertise and arsenal of tools from machine learning/computational statistics can be extremely powerful [10,3,4]. Informationtheoretic tools and pertinent concepts can be extremely useful [9].…”

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confidence: 99%